Why does multiplying by 10 shift each digit one place to left

Mathematics

2 answers:

Goryan [66]3 years ago

8 0

Answer:

because you're adding another zero which takes place in the place value chart.

Step-by-step explanation: For example 25 (initial value)

multiplied one time by ten : 250

250 multiplied by ten: 2,500

and on the place value chart here each new zero takes a new place which gives the 25 a new value.

lesya692 [45]3 years ago

6 0

Multiplying by 10 can be thought of as just adding a 0 to the right end of a number. If you have 2 and multiply it by 10, you get 20. For 1,234, you get 12,340. If you have 98,765, you can 987,650. Same thing applies for 100, 1000, 10000, ...., and so on. It moves it over depending on the number of 0's there are in the number. If it is 100, it will move two 0's over. For example, if you multiply 45 by 100, you get 4,500. The two zeros from 100 moved to the right side of the 45 to get 4500.

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Suppose a batch of metal shafts produced in a manufacturing company have a population standard deviation of 1.3 and a mean diame

lbvjy [14]

Answer:

54.86% probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 208, \sigma = 1.3, n = 60, s = \frac{1.3}{\sqrt{60}} = 0.1678$

What is the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

Lesser than 208 - 0.1 = 207.9 or greater than 208 + 0.1 = 208.1. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.

Lesser than 207.9.

pvalue of Z when X = 207.9. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{207.9 - 208}{0.1678}$